Question
Suppose an MRI scanner uses 100-MHz radio waves. (a) Calculate the photon energy. (b) How does this compare to typical molecular binding energies?
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Final Answer
  1. 4.14×107 eV4.14 \times 10^{-7}\textrm{ eV}
  2. The photon energy is about 4×1074 \times 10^{-7} times smaller than typical molecular binding energies.

Solution video

OpenStax College Physics for AP® Courses, Chapter 30, Problem 63 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. The energy of a photon is given by equation [29.13] which is Planck's constant times the frequency and we are told the frequency is 100 megahertz. So we go 100 times 10 to the 6 hertz multiplied by Planck's constant— 4.14 times 10 to the minus 15 electron volt seconds— giving an energy of 4.14 times 10 to the minus 7 electron volts. And then we compare that with representative energies for sub-microscopic effects and we see that the binding energy of a weakly bound molecule is about 1 electron volt. And so we take this photon energy, divide it by that and we get 4 times 10 to the minus 7. So the photon energy is about 4 times 10 to the minus 7 times smaller than typical molecular binding energies.